Mathematics · Primary 4

Active learning ideas

Factors and Multiples

Active learning helps students visualize the relationships between factors and multiples through movement and collaboration. When students pair up or work in teams, they can test ideas together and correct misunderstandings in real time. This hands-on approach builds confidence and deepens their understanding of number patterns.

• MOE Syllabus Outcomes
• MOE: Whole Numbers - P4

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 25 min · Pairs

Pairs: Factor Pairs Race

Pairs receive a two-digit number and race to list all factor pairs using mini-whiteboards, checking by multiplying back. Teacher calls time after 3 minutes; pairs swap numbers and repeat twice. Discuss systematic order from 1 up.

What is the difference between a factor and a multiple of a number?

Facilitation Tip

During Factor Pairs Race, remind pairs to start with 1 and its pair first to ensure systematic listing.

What to look for

Give students a card with two numbers, e.g., 18 and 24. Ask them to list all factors of 18, then list all factors of 24. Finally, ask them to identify the common factors and the LCM of 18 and 24.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 35 min · Small Groups

Small Groups: Multiples Chain Game

In groups of four, students sit in a circle and say the next multiple of two given numbers in turn, like 4 and 6. If stuck, pass a counter; first to LCM wins a point. Rotate roles and numbers for three rounds.

How do you find all the factors of a 2-digit number using systematic listing?

Facilitation Tip

For the Multiples Chain Game, set a timer for one minute per round to keep the energy high and focused.

What to look for

Write a list of numbers on the board (e.g., 1, 2, 13, 15, 19, 21). Ask students to hold up one finger for prime numbers and two fingers for composite numbers. Then, ask volunteers to explain their reasoning for two of the numbers.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 30 min · Whole Class

Whole Class: Prime Sort Relay

Divide class into two teams. Call a number; first student from each team runs to board, states if prime or composite with factors. Correct team scores; continue for 10 numbers, then review rules.

Can you identify the common multiples of two numbers and find the lowest common multiple?

Facilitation Tip

In the Prime Sort Relay, place a small timer at each station to encourage quick and accurate sorting.

What to look for

Pose this scenario: 'Sarah has 30 stickers and wants to share them equally among her friends. She also has 40 pencils and wants to put them into equal packs. What is the largest number of friends she can share stickers with so everyone gets the same amount? What is the largest number of pencils she can put in each pack so all packs are equal?' Guide students to identify the need for common factors.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Individual: LCM Puzzle Cards

Students match pairs of numbers to their LCM cards, using factor lists as clues. Self-check with answer key, then pair to explain one match. Extend by creating own puzzles.

What is the difference between a factor and a multiple of a number?

Facilitation Tip

With LCM Puzzle Cards, encourage students to use grid paper to sketch arrays if they struggle to visualize multiples.

What to look for

Give students a card with two numbers, e.g., 18 and 24. Ask them to list all factors of 18, then list all factors of 24. Finally, ask them to identify the common factors and the LCM of 18 and 24.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach this topic by connecting factors to division and multiples to multiplication through visual models. Avoid rushing to abstract rules; instead, let students discover patterns through hands-on activities. Research shows that using physical manipulatives or quick sketches helps students internalize these concepts more deeply than rote memorization.

Students will confidently list factors and multiples, distinguish between prime and composite numbers, and explain how these concepts connect multiplication and division. Small group discussions and relay races will show their ability to apply these skills in problem-solving contexts.

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Watch Out for These Misconceptions

• During Prime Sort Relay, watch for students who incorrectly label 1 as a prime number.

  Have students test 1 by trying to pair it with another factor beyond itself. Ask them to recall that prime numbers must have exactly two distinct factors, and 1 only has one. Use the sorting cards to physically move 1 out of the prime pile during the relay.

• During Factor Pairs Race, watch for students who confuse factors and multiples.

  Ask pairs to build rectangular arrays with grid paper for their numbers. For example, for 12, they should create arrays of 1x12, 2x6, and 3x4. This visually separates factors (the dimensions) from multiples (the total count of squares).

• During Multiples Chain Game, watch for students who assume the LCM is always the product of two numbers.

  Have groups use Venn diagrams on their whiteboards to list multiples side by side. Point out overlapping numbers, then ask them to divide the product by the GCF to find the LCM. This reinforces why the product isn't always the smallest shared multiple.

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Methods used in this brief

• Collaborative Problem-Solving